Reversibly formed bilayer vesicles: energetics and polydispersity

Model calculations based on the multiple equilibrium approach indicate that the spontaneous formation of geometrically closed bilayer vesicles is geared primarily by the bilayer tension which in turn is largely determined by the work of bending the bilayer into a spherical vesicle, and a statistical-mechanical factor that accounts for the fluctuations in composition, chain packing density and shape. We demonstrate that the free energy required to form a spherical vesicle is made up of two main contributions: the (size-independent) work of bending the constituent monolayers and the work of stretching the bilayer that is determined by the planar bilayer tension. A previously undiscovered contribution to the work of bending a vesicle bilayer, originating from geometrical packing constraints, is presented. On this basis we obtain vesicle size distributions with maxima located at radii several orders of magnitude larger than where the local free energy minima of the equilibrium vesicle actually occur. Moreover, according to our analysis, the relative width of a vesicle size distribution, σ R/R max, is generally at full equilibrium equal to 0.283, independently of the energetic vesicle parameters. Our calculations of the bending work of mixed SDS/dodecanol bilayers predict vesicles with R max in the range of 0.1–10 μm and for mixed anionic/cationic bilayers we obtain small unilamellar vesicles with R max<1000 Å when one of the surfactants is in excess, in good qualitative agreement with recent experimental findings.